A method for evaluating the power generation performance of a floating photovoltaic array

Abstract

The present application belongs to the technical field of photovoltaic power generation, and particularly relates to a floating photovoltaic array power generation performance evaluation method, comprising: constructing a near-shore sea area environment model; calculating a real near-shore wave field by using a Boussinesq model; constructing a matching surface on the outside of the array and extracting wave field time domain information, and converting the wave field time domain information into frequency domain components; taking the components as boundary conditions, and solving the six-degree-of-freedom motion response of the array by using a boundary element method; calculating the dynamic posture of the components, the solar incident angle, the out-of-plane irradiance, the working temperature and the instantaneous output power in real time based on the motion response; and finally evaluating the wave-induced power generation loss. The present application balances between the calculation efficiency and the accuracy by coupling the Boussinesq model and the boundary element method in a sub-domain nesting manner, simultaneously considers key environmental factors such as non-constant water depth, terrain undulation, shoreline effect and the like, and first realizes the chain coupling of "hydrodynamic force-light receiving-power generation", thereby providing reliable support for the engineering design and performance evaluation of the near-shore floating photovoltaic array.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic power generation technology, and specifically relates to a method for evaluating the power generation performance of a floating photovoltaic array. Background Technology

[0002] The global energy system is accelerating its transition to clean energy. Driven by both technological advancements in renewable energy and policy support, photovoltaic (PV) power generation has become one of the most competitive clean energy sources. To overcome land resource constraints, the application scenarios for PV power generation are gradually expanding to water areas. Floating PV systems, by deploying PV modules on the water surface, offer advantages such as land conservation and efficient water cooling, leading to rapid development. Among these, offshore floating PV systems, relying on the vast ocean space, are particularly suitable for nearshore waters. These areas typically have relatively mild sea conditions, are close to load centers, and facilitate operation and maintenance, making them a priority location for demonstration projects.

[0003] However, nearshore waters are characterized by dramatic changes in water depth, complex topography, and meandering coastlines. These factors cause significant nonlinear deformations in wave propagation, including refraction, diffraction, reflection, and energy accumulation, resulting in a complex wave field with highly non-uniform spatial distribution. In such a real marine environment, floating photovoltaic arrays, as multi-module coupled floating structures, are significantly affected by wave non-uniformity, topographic modulation effects, and interactions between modules. The dynamic attitude changes of the array under wave action alter the actual light-receiving angle of the photovoltaic modules, thereby affecting the received solar irradiance and power output.

[0004] Currently, performance evaluation methods for offshore floating photovoltaic arrays, especially those applicable to complex nearshore environments, still have the following prominent problems:

[0005] 1. Existing analytical methods oversimplify environmental assumptions, making it difficult to characterize the complex wavefield features near the coast.

[0006] Most existing engineering analysis methods are based on linear potential flow theory, which makes idealized assumptions about the marine environment and fails to reflect the complex characteristics of the real wave field near the coast. For example, prior art publication CN119623163A discloses a method for calculating the dynamic response of a pure float-type photovoltaic array. This method predicts the array's motion response by constructing a minimal repeating module and a numerical equivalent, combining frequency domain hydrodynamic calculations and time domain simulations. However, the specification of this document explicitly states that its hydrodynamic analysis is based on linear potential flow theory and assumes that "the water depth is constant." This simplification prevents it from considering key environmental modulation factors commonly found in nearshore waters, such as shallow water effects, seabed topography, and shoreline reflections, resulting in limited accuracy in predicting dynamic response under complex terrain. Similarly, prior art 2 (Xu et al., 2024, literature "Hydrodynamic performance study of floating photovoltaic arrays with multiple inter-module connections") studied the hydrodynamic response characteristics of floating photovoltaic arrays under multi-module connection conditions. It also adopted the traditional linear potential flow theory and assumed that the wave field was a small-amplitude linear wave. Its model "did not consider the influence of topographic changes on wave propagation", so it was difficult to capture the nonlinear deformation of waves and energy redistribution caused by topography in the actual nearshore environment.

[0007] 2. The power generation performance assessment is disconnected from the actual dynamic response and complex wave environment.

[0008] Existing solutions often treat structural dynamic analysis and power generation performance evaluation separately, or base power generation analysis on simplified environmental and motion responses. Existing technology 3, publication number CN120850735A, proposes a method for optimizing the power generation efficiency of a floating photovoltaic power generation system. Although it uses hydrodynamic simulation to obtain the platform's pitch angle and combines it with an irradiance model and optimization algorithm to improve power generation performance, its wave input is based on the assumptions of linear potential flow and regular waves, failing to consider the modulation effect of real nearshore topographic changes on the wave field. Therefore, the motion response upon which this method is based does not originate from a real complex wave environment. Although attitude factors are introduced, the coupling relationship between topography, waves, structure, and power generation is not established. It cannot accurately assess wave-induced power generation losses in specific nearshore environments, and it is even more difficult to cover multi-degree-of-freedom responses and the overall performance analysis of large-scale arrays in complex terrain, significantly limiting its applicability.

[0009] Existing technology 4, patent number CN119482449B, discloses a method for estimating the power generation of a floating photovoltaic system. This method uses regular waves combined with AQWA software for linear potential flow analysis, considering only simple wave incidence conditions and failing to account for the modulation effects of near-shore water depth variations, complex seabed topography, shoreline reflection, and artificial protective structures on the wave field, thus limiting its environmental applicability. Regarding structural analysis, this method only obtains the tilt angle of a single platform through floating body simulation, without establishing a systematic hydrodynamic analysis method for multi-module arrays, connectors, and mooring systems, and cannot characterize the multi-body coupling response of the array under non-uniform wave fields. In terms of power generation modeling, this method only calculates the maximum power generation under static conditions and then estimates it using the total radiant energy ratio. Essentially, it still belongs to the static power generation estimation combined with a simple reduction coefficient mode, without establishing a dynamic model based on time-evolved component attitude, POA irradiance, component temperature, and electrical output.

[0010] 3. High-precision models lack practical engineering applications due to excessively high computational costs.

[0011] Existing technology 5 (Engsig-Karup et al., 2009, "An efficient flexible-order model for 3D nonlinear water waves") proposes a three-dimensional variable-order nonlinear water wave model based on fully nonlinear potential flow theory. This model can capture nonlinear wave propagation, deformation, reflection, and diffraction phenomena under complex terrain and geomorphology, and can be used for fully coupled simulation of complex terrain, geomorphology, structure, and waves. This model has advantages in physical accuracy and can theoretically be used for wave-structure coupling analysis in complex environments. However, its reliance on fully nonlinear potential flow theory results in extremely high computational costs, making it difficult to adapt to the large-scale computational domains (hundreds of meters or even kilometers) corresponding to floating photovoltaic arrays. Furthermore, for multi-module array arrangements commonly seen in engineering practice, especially when considering nearshore wave propagation evolution and non-uniform responses between structures, large-scale, fully detailed simulation will lead to an exponential increase in computational resource consumption, making it difficult to meet the needs of rapid design, engineering optimization, and scheme evaluation under current computing power conditions.

[0012] In summary, existing technologies present a dilemma: methods represented by technologies 1, 2, 3, and 4 prioritize computational efficiency for engineering applications, but sacrifice simulation accuracy in complex nearshore terrain by simplifying environmental assumptions, and fail to achieve a tight coupling evaluation of wave-structure-power generation; methods represented by technology 5, while achieving breakthroughs in physical accuracy and handling complex terrain and nonlinear waves, suffer from high computational costs, making them difficult to directly apply to the engineering design and optimization processes of large floating photovoltaic arrays. Currently, the field lacks an integrated technical solution that can accurately characterize complex nearshore terrain and nonlinear wave propagation within an engineering-acceptable computational cost, and achieve a chain-coupled evaluation of wave environment, structural dynamic attitude, and photovoltaic power generation performance. Summary of the Invention

[0013] To address the shortcomings of existing technologies that rely on idealized seabed and wavefield assumptions, failing to reflect the actual nearshore wave propagation, topography, and the impact of structures on array attitude, and suffering from high computational costs and unsuitability for large-scale marine engineering applications, this invention proposes a method for evaluating the power generation performance of floating photovoltaic arrays that considers complex marine environments and dynamic attitude changes. The method includes the following steps:

[0014] A method for evaluating the power generation performance of a floating photovoltaic array includes the following steps:

[0015] S1. Obtain and construct an environmental model of the nearshore sea area where the floating photovoltaic array is deployed. The environmental model includes at least two-dimensional spatially distributed water depth and topographic data, shoreline geometry and / or information on artificial protective structures.

[0016] S2. In the outer domain of the nearshore sea area, the fully nonlinear Boussinesq wave model is used to calculate the real nearshore wave field that includes temporal and spatial evolution.

[0017] S3. Construct a matching surface outside the inner domain of the floating photovoltaic array, extract the time domain information of the wave field at the matching surface from the real nearshore wave field described in step S2, and convert it into frequency domain wave components.

[0018] S4. Using the frequency domain wave components obtained in step S3 as the incident wave boundary conditions, a three-dimensional linear hydrodynamic analysis method based on the boundary element method is adopted to solve the six-degree-of-freedom motion response of each module of the floating photovoltaic array in the inner domain computational domain.

[0019] S5. Based on the six-degree-of-freedom motion response time history of each module obtained in step S4, calculate the dynamic spatial attitude of each photovoltaic module in real time, and then calculate the solar radiation incident angle, out-of-plane irradiance, module operating temperature and instantaneous electrical output power of each photovoltaic module in sequence.

[0020] S6. Quantitatively assess wave-induced power generation loss.

[0021] Furthermore, step S4 specifically includes:

[0022] S41. Establish a computational boundary that includes the wet surface, free surface, matching surface and seabed surface of all modules in the array, and discretize it into a surface mesh;

[0023] S42. Based on the boundary element method with simple Green's function, solve the boundary integral equations corresponding to the scattering potential and the radiation potential to obtain the source intensity on each surface element.

[0024] S43. Calculate the wave excitation force, added mass coefficient, and radiation damping coefficient acting on each module based on the source intensity.

[0025] S44. Combining the array's mass, still water recovery stiffness, mooring stiffness, and connector stiffness, construct and solve the multi-module coupled motion equations to obtain the six-degree-of-freedom motion response of each module.

[0026] Furthermore, step S5 also includes summarizing the total output power of the array, and in step S6, the wave-induced power generation loss rate is calculated based on the total output power of the array and the theoretical output power under static conditions.

[0027] Furthermore, the calculation of the dynamic spatial attitude of each photovoltaic module in step S5 specifically involves: calculating the dynamic normal vector of the photovoltaic module in the global coordinate system through coordinate transformation based on the roll, pitch, and yaw angles of the module, thereby obtaining the dynamic tilt angle and azimuth angle.

[0028] Furthermore, the total output power of the array is first calculated based on the out-of-plane irradiance and the component operating temperature to obtain the instantaneous efficiency of the component, then combined with the light-receiving area of ​​the component to obtain the output power of a single component, and finally the output power of all components is summed to obtain the total output power of the array.

[0029] Furthermore, the governing equations of the fully nonlinear Boussinesq wave model explicitly include a spatially varying two-dimensional depth function to simulate the modulation effects of non-constant water depth, topographic relief, shoreline reflection, and artificial structures on the waves.

[0030] Furthermore, in step S3, the time-domain information of the wave field at the matching surface is converted into frequency-domain wave components using the Prony-SS decomposition method.

[0031] Furthermore, the formula for calculating wave-induced power generation loss (WIL) in step S6 is as follows:

[0032] ;

[0033] in, The theoretical power is assumed to be when the platform is stationary. To account for the actual power after dynamic response.

[0034] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0035] This invention constructs a domain-nested solution system based on a shallow-water Boussinesq wave propagation model and a three-dimensional boundary element hydrodynamic model. While the Boussinesq equations can effectively characterize the nonlinear propagation and evolution of nearshore waves under complex terrain conditions, they rely on depth integrals such as free surface elevation and depth-average velocity as fundamental unknowns and require continuous evolution of the free surface. Therefore, they lack the ability to directly solve for the hydrodynamic response and six-degree-of-freedom motion of the floating body at the governing equation level. This invention, through a domain-nested approach, uses the outer domain Boussinesq calculation to provide the real nearshore wave field, and then employs a three-dimensional hydrodynamic model in the inner domain to solve for the array module response. This allows for the simultaneous consideration of key hydrodynamic modulation factors such as non-constant water depth, complex seabed topography, shoreline refraction and reflection effects, interference from artificial protective structures, and wave energy focusing, significantly improving the accuracy of motion response prediction for floating photovoltaic arrays in real-world deployment areas.

[0036] In addition, the domain-nested computational framework effectively overcomes the bottleneck that global CFD or fully nonlinear potential flow models are difficult to apply to the evaluation of arrays on the scale of hundreds to thousands of meters due to their high computational cost. At the same time, it avoids the problems of rapid expansion of matrix size and excessive consumption of resources caused by directly extending the boundary element method to large-scale computational domains.

[0037] This invention realizes the chain coupling of "hydrodynamic response - light-receiving conditions - electrical output" for floating photovoltaic arrays at sea, and maps the real-time attitude changes of the structure to the tilt angle, azimuth angle, out-of-plane irradiance, temperature correction and instantaneous output power. It can be used to quantitatively evaluate wave-induced power generation loss and spatial power generation differences, and provide engineering with more reliable power generation performance prediction results than traditional static or fixed tilt angle models. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the numerical calculation part of an embodiment of the present invention. Figure 1 ;

[0039] Figure 2 This is a schematic diagram of the numerical calculation part of an embodiment of the present invention. Figure 2

[0040] Figure 3 This is the discrete surface element mesh of the hydrodynamic analysis module in this embodiment of the invention;

[0041] Figure 4This paper compares the differences in local wave loads (six degrees of freedom, dimensionless) of a floating photovoltaic array calculated by the method of this invention and the traditional potential flow method under the influence of oblique wave incidence and complex terrain. Detailed Implementation

[0042] The performance evaluation of nearshore floating photovoltaic arrays depends not only on the array's own characteristics but also, more critically, on the complex nearshore hydrodynamic environment. Existing evaluation methods suffer from the dual contradiction of physical distortion and high computational cost. This invention shifts from seeking a single all-around model to constructing a complementary and synergistic computational system. It recognizes that the Boussinesq wave model excels at large-scale nearshore nonlinear wave propagation, while 3D BEM hydrodynamic analysis excels at the fine dynamic response of local floating arrays. These two models are physically complementary, but a theoretical gap exists when directly combining them.

[0043] The Boussinesq model, based on the shallow-water long-wave approximation, outputs depth-averaged time-domain physical quantities; while the BEM, based on potential flow theory, requires satisfying the three-dimensional velocity potential or equivalent boundary conditions of the Laplace equation. The two models differ fundamentally in their governing equations and variable definitions, making direct interoperability impossible. This invention extracts complete time-history information of velocity and dynamic pressure on the matching surface and, through the Prony-SS identification method, decomposes and reconstructs the nonlinear, non-stationary time-domain signal into a set of equivalent linear frequency-domain components that maintain consistency with the original wavefield in energy, phase, and dominant spectral structure. This "generates" a physically equivalent, understandable real wavefield input for the linear hydrodynamic solver, resolving the fundamental incompatibility between the models.

[0044] Furthermore, nearshore array simulations need to cover sea areas ranging from hundreds to thousands of meters in depth. Using a high-precision method across the entire domain is computationally infeasible; using a simplified method results in insufficient accuracy. This invention employs a nested domain modeling strategy. The outer domain uses the computationally efficient Boussinesq model to handle large-scale topographic and wave evolution; the inner domain uses BEM to finely solve the array response. By setting unidirectional coupling and absorbing boundary conditions on the matching surface, the resource consumption of full-domain computation is effectively avoided, while ensuring high physical accuracy of the inner domain input.

[0045] Considering that waves and power generation belong to different time scales and disciplines, minute errors in attitude can be nonlinearly amplified through geometric-optical relationships, leading to severe distortion in power generation predictions. Data synchronization and spatial mapping of multi-module arrays are also extremely complex. In this invention, all subsequent calculations (light reception, temperature rise, power generation) strictly use the array attitude sequence solved by the hydrodynamic module as input, forcibly following the physical sequence of "waves—attitude—light reception—electrical output." Each step is instantaneously mapped based on a clear physical model, ensuring the rigor and traceability of the entire logical chain.

[0046] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0047] This embodiment proposes a method and system for evaluating the power generation performance of a floating photovoltaic array, as detailed below:

[0048] I. System Structure

[0049] This invention mainly consists of the following three parts:

[0050] The preprocessing module includes: a marine environment modeling module (acquiring and reconstructing information on seabed topography, water depth distribution, shoreline and artificial structures); an array structure modeling module (defining parameters for modular floating bodies, connecting devices and mooring systems); and an environmental and meteorological input module (preparing data such as waves, tides, solar irradiance, temperature, and wind fields).

[0051] The numerical calculation section includes: a wave propagation simulation module (a fully nonlinear Boussinesq shallow water wave propagation model used to generate a realistic nearshore wave field that takes into account topographic modulation effects); a hydrodynamic analysis module (using the calculation results from the wave propagation simulation module to perform three-dimensional boundary element calculations, solve the array's six-degree-of-freedom motion equations, and obtain the dynamic attitude changes of each module); a power generation performance evaluation module (calculating POA irradiance, module temperature, electrical output, and array power based on dynamic attitude); and a wave-induced power generation loss evaluation module (comparing static steady-state conditions with dynamic wave conditions to quantify the WIL index).

[0052] The post-processing and data analysis modules include: a numerical results visualization module (wavefield evolution, motion response, power time history, spatial power generation impact distribution, etc.); an array structure safety verification module (motion amplitude, mooring tension, fatigue and extreme survivability assessment); and a nearshore site adaptability and optimization module (based on a comprehensive assessment of topography, water depth, wavefield, power generation efficiency and WIL).

[0053] Each module operates collaboratively based on a unified data interface, forming a complete workflow from marine environment modeling, wave propagation simulation, hydrodynamic response solving to quantitative evaluation of power generation performance and engineering decision support. This system can not only realistically reflect the multi-field coupling relationship between topography, waves, structure, and power generation in complex nearshore environments, but also directly serve engineering site selection and design optimization.

[0054] II. Specific Operation Process

[0055] 1. Pre-processing

[0056] Before conducting numerical simulations, it is necessary to acquire and organize basic information about the deployment area of ​​the floating photovoltaic array project, and complete the model input construction through the preprocessing module, specifically including:

[0057] The marine environment modeling module is used to reconstruct the realistic nearshore hydrodynamic environment. The main inputs include: water depth and seabed topography data (measured data or obtained from a topography database), which are then used to form a discrete two-dimensional water depth matrix. Coastline morphology and geomorphological features; information on nearshore artificial protection or marine structures (such as submerged breakwaters, groynes, diversion dikes, floating breakwaters, etc.).

[0058] If the protective structure weakens wave energy by changing the terrain (such as a submerged breakwater), it is directly included in the water depth matrix; if it is a floating breakwater, equivalent reflection / damping boundary conditions can be set in the Boussinesq model according to its reflection or dissipation characteristics, and the reflection coefficient can be estimated by the Goda two-point method to achieve equivalent modeling.

[0059] The array structure modeling module is used to establish the structural mathematical model of the floating photovoltaic array. Inputs include: the geometric dimensions, draft, mass, center of mass, and moment of inertia of each floating module; the array arrangement and topological relationships between modules; the stiffness, damping, and arrangement of connectors; and mooring system parameters (cable material, length, pretension, anchoring method, and spatial arrangement). The module outputs a discrete surface element model for boundary element analysis, an equivalent generalized mass matrix, and a restoring stiffness matrix, and generates connection and mooring constraint matrices.

[0060] The environment and meteorological input module is used to construct the environmental driving conditions required for multi-field coupling analysis. The input content includes: wave elements (significant wave height, main period, peak frequency, wave direction, spectrum, return period, etc.); tidal and water level changes; solar irradiance (DNI, DHI, GHI), solar altitude angle and azimuth angle data; and meteorological parameters such as temperature, wind speed, and humidity.

[0061] The aforementioned data is used to drive wave propagation simulation, array dynamic response, and subsequent power generation performance evaluation. Through these three preprocessing modules, the marine environmental field, structural parameter system, and multi-source environmental excitation required for subsequent numerical calculations can be systematically generated.

[0062] 2. Numerical Calculation

[0063] This invention establishes a multi-field coupled numerical calculation framework that spans "real sea area—wave propagation—hydrodynamic response—attitude change—component light reception—electrical output," and the overall process is as follows:

[0064] (1) Wave propagation simulation module performs complex nonlinear wave propagation

[0065] Within an external computational domain covering the actual deployment area, a second-order fully nonlinear Boussinesq model is used to simulate the evolution of real nearshore waves. Inputs include: a two-dimensional water depth matrix and seabed topography; shoreline geometry; artificial structures such as submerged breakwaters, offshore breakwaters, and floating breakwaters; and sea state information such as wind / wave / swell / multi-peak spectrum. The core governing equations are expressed as follows:

[0066]

[0067]

[0068] in: : Horizontal two-dimensional spatial coordinates; Time variable; : Horizontal gradient operator; : Horizontal divergence operator; subscript Regarding time The partial derivatives; : Free surface changes; Instantaneous water depth; Local water depth; For reference position The horizontal velocity vector at point . Vertical coordinates, with upward as positive; : The vertical coordinate position of the reference velocity layer;

[0069] ;

[0070] ;

[0071] ;

[0072] in, : The second-order dispersion correction term introduced by the vertical velocity distribution; : A higher-order nonlinear correction term caused by the combined effects of nonlinear convection and dispersion;

[0073] The output of the wave propagation simulation module is: the real nearshore wave field that varies with time. and Then, the matching surfaces need to be configured. (refer to Figure 1 and Figure 2 Time-domain wave field information at ) Extraction is performed, and these four terms represent the three-dimensional velocity components and dynamic pressure time series at the matching surface, respectively, calculated according to the following formula and combined with the discrete surface element information generated by the array modeling module:

[0074] ;

[0075] ;

[0076] ;

[0077] in, : Horizontal velocity component; Vertical velocity component; Dynamic pressure; Auxiliary quantities related to the law of conservation of mass; : Reference layer velocity divergence term; Gravitational acceleration; Fluid density;

[0078] Subsequently, matching surfaces Wave field information at the location Transformed into a matching surface through Prony-SS decomposition. Frequency domain wave field information This serves as the boundary condition for the subsequent boundary element hydrodynamic analysis module, thereby enabling the transfer of wave field information from the external region to the internal region.

[0079] This embodiment's wave propagation simulation module achieves accurate simulation of nearshore wave refraction, diffraction, reflection, and nonlinear evolution by directly embedding the real two-dimensional water depth matrix into the Boussinesq equations and explicitly physical modeling the shoreline and protective structures. The output spatiotemporal wave field, after being extracted by a matching surface, is transformed into spatially differentiated frequency domain boundary conditions. This provides physically realistic, non-uniform wave input for subsequent hydrodynamic analysis, fundamentally replacing the uniform wave field assumption of traditional methods and becoming a crucial bridge connecting the real terrain environment with the array's dynamic response.

[0080] (2) The hydrodynamic analysis module performs fluid-structure interaction solution.

[0081] The hydrodynamic calculation module uses the surface element method based on the simple Green's function to solve for the array hydrodynamic coefficients, loads, and motion response. The detailed steps are as follows.

[0082] Suppose the array contains N modules, and the boundary of the hydrodynamic computational domain includes the wetted surfaces of the N modules. Free surface Matching surface and seabed Assuming the floating photovoltaic array is situated in a viscosity-free, incompressible fluid, the fluid motion can be described by the velocity potential satisfying the Laplace equation. Total velocity potential This can be expressed using the superposition principle as follows:

[0083] ;

[0084] in represents the real part of the variable; i is the imaginary unit; e is the natural base; ω is the wavy angular frequency; It is a three-dimensional spatial position vector; It is a scattering potential; (𝑗=1,2,...,6,𝑚=1,2,...,𝑁) is the unit amplitude radiation potential of the m-th floating module in the j-th degree of freedom direction; (𝑗=1,2,...,6,𝑚=1,2,...,𝑁) is the motion amplitude of the m-th floating module in the j-th degree of freedom direction;𝑁 is the total number of floating photovoltaic floating modules in the array.

[0085] The boundary conditions satisfied by the scattering potential are:

[0086] ;

[0087] in, is the normal vector pointing to the outside of the computational domain; g is the gravitational acceleration; Let be the wetted surface boundary of the m-th floating module; This is the boundary of the free liquid surface; It is the seabed boundary; This is the matching surface between the outer and inner domains.

[0088] The boundary condition satisfied by the unit amplitude radiation potential of the m-th floating body module in the j-th degree of freedom direction is:

[0089] ;

[0090] in, The wetted surface boundaries of the remaining floating body modules; The local wave number is calculated based on the local water depth. The horizontal radial distance; Let be the generalized unit normal vector pointing inwards from the wetted surface, where It is a wet surface The position vector on.

[0091] After the scattering potential is solved, the wave excitation force acting on the m-th floating body module in the i-th degree of freedom direction is... Calculated based on the integral of Bernoulli's equation over each wet surface:

[0092] ;

[0093] Furthermore, the radiation hydrodynamics of the m-th floating module in the i-th degree of freedom direction Represented as:

[0094] ;

[0095] in, It is the additional mass coefficient of the m-th floating body module in the i-th direction caused by the oscillating motion of the n-th floating body module in the j-th direction; This is the damping coefficient, where the subscripts and superscripts are defined the same as those for the added mass coefficient. The added mass coefficient and damping coefficient can be expressed as:

[0096]

[0097] in, The imaginary part of the radiation potential in the j-direction is given, while It indicates that it is actually part.

[0098] According to Newton's second law, the dynamic behavior of a floating photovoltaic array composed of multiple floating modules can be expressed as a multi-module coupled motion equation:

[0099]

[0100] in, The generalized mass matrix element of the m-th floating body; This is the overall stiffness matrix between the m-th and n-th floating body modules, including the hydrostatic restoring force. Mooring stiffness Connector stiffness The overall stiffness matrix is ​​defined as follows:

[0101]

[0102] in, The still water restoring force matrix applies only to the m-th buoy; This is the mooring stiffness matrix, which only applies to the m-th floating body; Contributes to the stiffness of the connecting parts of the m-th floating body; Let be the stiffness of the connection between the m-th and n-th floating bodies.

[0103] like Figure 3 As shown, the array structure modeling module has discretized each surface into a surface mesh. Assuming the source density... On each surface element mesh distributed on the boundary surface, among which Let be the displacement vector of the source points on the boundary surface. The potential function in the fluid domain is represented by the source density distribution on the boundary:

[0104] ;

[0105] in It is the position vector of any field point within the fluid domain; It is the boundary surface of the entire computational domain (including each wetted surface, free liquid surface, mating surface and seabed boundary); It is a simple Green's function.

[0106] Differentiating both sides of the above equation and applying it to the centroid of each facet element yields a set of linear equations:

[0107] ;

[0108] Where S is the boundary surface with the source point q as the integration variable; The total number of face elements; Let be the centroid position of the m-th face element; Let m be the normal derivative along the direction normal to the outside of the m-th surface element; The source density on the nth surface element is unknown.

[0109] After substituting the corresponding boundary conditions for the radiation potential and scattering potential into the equation, and then rearranging and combining them, we obtain a condition regarding the source intensity. contain A system of linear equations with several unknowns is used to solve for the source intensity on each surface element. After solving for the source intensity on each surface element, the values ​​of various potential functions within the watershed can be obtained, thereby solving for parameters such as wave excitation force, added mass, and damping coefficient. Finally, the six-degree-of-freedom motion response of each module, the tension of the connecting parts, and the mooring tension are obtained by solving the equations of motion.

[0110] This module employs the boundary element method based on a simple Green's function, successfully accommodating the equivalent frequency domain boundary conditions derived from the real nonlinear wave field provided by upstream wave simulation. By solving the integrated motion equations that include radiation / scattering potential, multibody hydrodynamic interference, and the coupling of the entire system, it achieves refined solutions for the six-degree-of-freedom motion response, connector loads, and mooring tension of large-scale floating photovoltaic arrays under complex nearshore wave conditions, ensuring physical realism while also considering the feasibility and stability of engineering calculations.

[0111] (3) The photovoltaic power generation performance evaluation module calculates the array power generation efficiency.

[0112] Considering that waves and power generation belong to different time scales and disciplines, minute errors in attitude can be nonlinearly amplified through geometric-optical relationships, leading to severe distortion in power generation predictions. Data synchronization and spatial mapping of multi-module arrays are also extremely complex. In this invention, all subsequent calculations (light reception, temperature rise, power generation) strictly use the array attitude sequence solved by the hydrodynamic module as input, following the physical sequence of waves—attitude—light reception—electrical output. Each step is based on a well-defined physical model for instantaneous mapping, ensuring the rigor and traceability of the entire logical chain.

[0113] (A) Component pose extraction

[0114] Let the motion response of the m-th floating module at time t be:

[0115] ;

[0116] in: The translation amount is in meters. The values ​​are the roll, pitch, and bow angles (rad). At this point, the dynamic normal vector of the photovoltaic module (assuming static horizontal installation, i.e.) ):

[0117] ;

[0118] Therefore, the dynamic tilt angle and azimuth angle are respectively:

[0119] ;

[0120] ;

[0121] (B) Calculation of the Sun's Position

[0122] Given latitude Hour angle With solar declination Solar altitude angle:

[0123] ;

[0124] Sun azimuth:

[0125] ;

[0126] (C) Calculation of Angle of Incidence (AOI)

[0127] Define the direction vector of sunlight. Then the angle between the ray vector and the normal vector is:

[0128] ;

[0129] (D) Out-of-plane irradiance (POA)

[0130] Total out-of-plane irradiance from direct sunlight ,scattering Reflected by the sea surface composition:

[0131] ;

[0132] in:

[0133] ;

[0134] Sky diffuse irradiance (Hay–Davies model):

[0135] ;

[0136] Sea surface reflected irradiance:

[0137] ;

[0138] in: Direct irradiance; This refers to the diffuse irradiance. Total horizontal irradiance; seawater reflectivity

[0139] (E) Component operating temperature (NOCT model)

[0140] ;

[0141] in: For component temperature; Ambient air temperature; NOCT stands for Nominal Operating Cell Temperature.

[0142] (F) Electrical output of photovoltaic modules

[0143] Component instantaneous efficiency:

[0144] ;

[0145] Component output power:

[0146] ;

[0147] Total array output power:

[0148] ;

[0149] in: The nominal efficiency of the component; The component temperature decay coefficient; This refers to the light-receiving area of ​​the component.

[0150] (J) Wave-induced power generation loss assessment module calculates wave-induced power generation loss.

[0151] Wave-Induced Loss (WIL):

[0152] ;

[0153] in: This is the theoretical power assuming the platform is stationary; To account for the actual power after dynamic response.

[0154] 3. Post-processing and data analysis

[0155] The post-processing and data analysis module is mainly used to transform numerical calculation results into engineering-interpretable information, providing support for design, optimization, and decision-making. It includes: a numerical results visualization module, a wave-induced power generation loss assessment module, and a nearshore site adaptability and optimization module.

[0156] The numerical results visualization module is used to display key numerical outputs in multiple formats, including: the spatial evolution process of the nearshore wavefield ( Energy focusing, diffraction and refraction distribution); time history, spectrum and response amplitude of the six degrees of freedom motion of each module in the array; cloud map of force distribution of connectors, mooring tension and dynamic pressure; time series curves of power generation of single module and the whole array; thermal map of spatial difference in power generation in the array plane.

[0157] The array structure safety verification module, based on national and industry standards (such as design standards for floating photovoltaic systems, hydraulic structures, and mooring systems), completes the following indicator evaluations: motion amplitude, maximum tension of mooring cables, fatigue life and safety margin calculations; assessment of stress, displacement and failure risks of connectors; and analysis of extreme sea conditions, survivability and instability modes.

[0158] The nearshore site adaptability and optimization module, based on wave propagation and dynamic power generation analysis results, conducts quantitative comparisons of multiple candidate sea areas, including: evaluation of topography, water depth and construction feasibility; analysis of wave field non-uniformity, energy focusing and extreme risks; estimation of power generation potential in typical meteorological years; assessment of wave-induced power generation loss (WIL); and analysis of grid connection, operation and maintenance conditions and cost constraints.

[0159] Finally, site classification and recommended deployment areas are provided to support project planning decisions.

[0160] Figure 4 To compare the differences between the local wave load (dimensionless) of the floating photovoltaic array calculated by this method and the traditional potential flow method under oblique incidence and complex terrain, after the wave field undergoes refraction, reflection and strong nonlinear deformation, Figure (a) shows the load spectrum, which is a comparison of the force amplitude of different frequency components, which can reflect the contribution of each wave component to the structural force, and (b) shows the time-domain load variation curve.

[0161] Figure 4 As can be seen, the proposed method closely matches the true values. The method almost completely overlaps with the true response in both the time and frequency domains, maintaining accuracy even under complex nearshore conditions involving wave refraction, reflection, and strongly nonlinear propagation evolution. This demonstrates that the proposed method is applicable to load calculations under real sea conditions. Figure 4As shown in (a), the traditional potential flow method cannot accurately estimate the linear components of the force under oblique wave and nonlinear propagation conditions. The linear component in the heave direction is overestimated by nearly 50%, and there is also a significant deviation in the roll direction, indicating that the traditional method has a systematic error in this type of environment. In addition, due to the changes in propagation direction and energy redistribution caused by the terrain, the array exhibits a decrease in the linear components of roll and heave, and a significant increase in the higher-order harmonic components in the bow direction. These key nonlinear force characteristics cannot be obtained by the traditional method, while our method can fully identify and quantify them.

[0162] In summary, this method can not only accurately predict local load response, but also identify multi-directional propagation and nonlinear wave evolution characteristics that are missed by traditional methods, thereby significantly improving the reliability of wave load prediction and laying the foundation for subsequent structural safety and power generation performance assessment.

[0163] The embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for evaluating the power generation performance of a floating photovoltaic array, characterized in that, Includes the following steps: S1. Obtain and construct an environmental model of the nearshore sea area where the floating photovoltaic array is deployed. The environmental model includes at least two-dimensional spatially distributed water depth and topographic data, shoreline geometry and / or information on artificial protective structures. S2. In the outer domain of the nearshore sea area, the fully nonlinear Boussinesq wave model is used to calculate the real nearshore wave field that includes temporal and spatial evolution. S3. Construct a matching surface outside the inner domain of the floating photovoltaic array, extract the time domain information of the wave field at the matching surface from the real nearshore wave field described in step S2, and convert it into frequency domain wave components. S4. Using the frequency domain wave components obtained in step S3 as the incident wave boundary conditions, a three-dimensional linear hydrodynamic analysis method based on the boundary element method is adopted to solve the six-degree-of-freedom motion response of each module of the floating photovoltaic array in the inner domain computational domain. S5. Based on the six-degree-of-freedom motion response time history of each module obtained in step S4, calculate the dynamic spatial attitude of each photovoltaic module in real time, and then calculate the solar radiation incident angle, out-of-plane irradiance, module operating temperature and instantaneous electrical output power of each photovoltaic module in sequence. S6. Quantitatively assess wave-induced power generation loss.

2. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 1, characterized in that, Step S4 specifically includes: S41. Establish a computational boundary that includes the wet surface, free surface, matching surface and seabed surface of all modules in the array, and discretize it into a surface mesh; S42. Based on the boundary element method with simple Green's function, solve the boundary integral equations corresponding to the scattering potential and the radiation potential to obtain the source intensity on each surface element. S43. Calculate the wave excitation force, added mass coefficient, and radiation damping coefficient acting on each module based on the source intensity. S44. Combining the array's mass, still water recovery stiffness, mooring stiffness, and connector stiffness, construct and solve the multi-module coupled motion equations to obtain the six-degree-of-freedom motion response of each module.

3. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 1, characterized in that, Includes the following steps: Step S5 further includes summarizing the total output power of the array. In step S6, based on the total output power of the array and the theoretical output power under static conditions, the wave-induced power generation loss rate is calculated.

4. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 1, characterized in that, The calculation of the dynamic spatial attitude of each photovoltaic module in step S5 specifically involves: calculating the dynamic normal vector of the photovoltaic module in the global coordinate system through coordinate transformation based on the module's roll, pitch, and yaw angles, thereby obtaining the dynamic tilt angle and azimuth angle.

5. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 3, characterized in that: The total output power of the array is first calculated based on the out-of-plane irradiance and the component operating temperature to obtain the instantaneous efficiency of the component, then combined with the light-receiving area of ​​the component to obtain the output power of a single component, and finally the total output power of the array is obtained by summing the output power of all components.

6. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 1, characterized in that: The governing equations of the fully nonlinear Boussinesq wave model explicitly include a spatially varying two-dimensional depth function to simulate the modulating effects of non-constant water depth, topographic relief, shoreline reflection, and artificial structures on the waves.

7. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 1, characterized in that: In step S3, the time-domain information of the wave field at the matching surface is converted into frequency-domain wave components using the Prony-SS decomposition method.

8. The method for evaluating the power generation performance of a floating photovoltaic array according to claim 1, characterized in that: The formula for calculating wave-induced power generation loss (WIL) in step S6 is as follows: ； in, The theoretical power is assumed to be when the platform is stationary. To account for the actual power after dynamic response.

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